I open the Administrator group, then press "Add..." I gave the username
under Enter the object names to select Click on check names gave Domain
admin username and Password. its then Name not found Window came.

I then deleted the user account from domain controller recreated the same
but still have name not found error. I could add other useraccounts to the
same PC

Consequently, I cannot add a domain account to the local Administrators
group.

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Is the XP joined to the domain? Are you logged in as a domain admin to the XP? Does the Add wizard show it is looking in the domain or is it the local computer, and for Users not computers or other objects?

It was another domain user's PC. So it already joined to domain. Now I want
to change the Pc for another new user.I logged off the existing user. and
login as Local Administrator not domain administrator and tried to add new
user account to the PC. The add wizard showing it is looking in the domain
and yes for Users!